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Appropriate Mappings


Vox Article on viral memes and charitable giving

First, a disclaimer. This is not a post about the actual issues this article raises; just about the presentation of those claims. The image from the article has appeared in numerous places and been referenced by a number of news sources, as well as appearing in my Facebook and twitter feeds.

And it’s a bad image.

One minor issue is that it is hard to work out which circle relates to which disease, as the name of the disease only appears on the legend, so you are constantly moving your eyes from grey dot on left to the legend, to the grey dot on the right. Hard to make much sense. The fact that the legend doesn’t seem to have any order to it doesn’t help either. If this were 20 diseases instead of eight, the chart would be doomed!

Kudos for picking appropriate colors though. It helps that they used a natural mapping (pink <–> breast cancer; red <–> AIDS) that might help a bit.

The more worrying issue is that it makes a classic distortion mistake; look at the right side and rapidly answer the question, using just the images, not the text: “How many more deaths are there due to the purple disease than the blue disease?” 

Using the image as a guide, your answer is likely to be in the range 10 to 20 times as man, because the ratio of the areas is about that amount. When you look at the text, though, it’s actually only about four times. The numbers are not encoding the area, which is what we see, but they are encoding the radius (or diameter) which we do not immediately perceive.

The result is a sensationalist chart. It takes a real difference, but sensationalizes it by exaggerating the difference dramatically. If you want to use circles, map the variable of interest to AREA, not RADIUS. It fits our perceptions much more truthfully. It’s not actually perfect; we tend to see small circles as larger than they really are; but it’s much, much better).

So, here’s a reworking:

WhereWeDonate Vs. Diseases That Kill

I tried to keep close to the original color mappings, as they are pretty good, but have used width to encode the variable of interest, keeping the height of the rectangle fixed. I also labeled the items on both sides so we can see much more easily that heart disease kills about 4x as many people as Chronic Obstructive Pulmonary Disease. 

I also added some links between the two disease rankings to help visually link the two and aid navigation. The result is, I believe, not only more truthful, but easier to use. In short, it works.

Comics and Visualization

Understanding Comics book cover; Scott McCloudComics and Visualization

Although this book is over a decade old now (and Scott has a number of later books that follow on from this one), this is still a highly valuable book to read, getting great review from famous artists as a fundamental resource for comic book writers. I read this from the perspective of a visualization expert, and found a number of interesting points in the book, especially the earlier sections. He defines comics as “juxtaposed pictorial and other images in deliberate sequence, intended to covey information and/or to produce an aesthetic response in the viewer (p.9)”, which, to my mind, allows many visualizations to fits his definition! The concept of small multiples, when presented in a “deliberate order” such as via a trellis display, fits particularly well into this definition, so I was encouraged to read on. Some highlights of the book, from my point of view:

  • The use of simpler icons / symbols to make depictions of reality more universal; that argument resonates more strongly with me than Tukey’s data-ink concept. I feel more convinced by the argument that additional detail is bad when it makes it harder for us to understand the high-level picture because it draws us too much into the physicality of the shapes being used.
  • McCloud presents a triangular space, the vertices of which are “reality”, “language” and “the picture plane” into which comic styles can be placed. I think there is also value in looking at various styles of visualization and seeing where they fit in. Treemaps, for example, have more “realistic” versions using cushions, while keeping the same structure. Scientific, geographic or fluid display visualizations are more realistic than, say, statistical graphics.
  • Less is More” applied to the number of intermediate representations used — this argues that for visualizations of, say, a process evolving over time, we should not simply slice at even times, but instead look for important features we want to show, and show fewer frames.
  • Lots of good stuff on how time is perceived when displayed at a sequence.
  • Can Emotions be Visible?” is the motivating question for chapter five — I would be very curious to see if we could apply his ideas to visualizations — maybe people like pie charts because they seem warm, serene and quiet, whereas a line chart with gridlines is rational, conservative and dynamic?

As an aside, I included a comic in my book on Visualizing Time, more as a whimsy than anything else, but I’m glad that I have at least a tenuous link with Scott McClouds’s highly recommended book! comics

Every Now and Again, a Pie can be Good

It is hard to find anyone in visualization today with much time for pie charts. In fact it seems de rigueur to disdain them. And yet we see an awful lot of them. Now, I’m not going to claim that they are a good, general purpose chart, but I do always like to think of times when a chart will actually work well.

When Pie Charts Work At All

One well-known requirement for a pie to have a chance of working is that the data represent a fraction of a whole. That’s the big selling point of pie charts — each data row should represent a fraction of the overall data. So pies work best for percentages and fractions, and second-best for counts, populations, weights — things for which there is a natural feeling that summing them all up and saying “that represents 100%” is good.

On the side of evil is when the numbers must not be summed — if the data represent means (for different sized groups) or degrees Fahrenheit, then a pie representation is flat-out wrong. It’s not a bad rule to say:

Only Use a Pie if it makes sense to think of the data values as summing to 100%

The second rule I’d suggest is based on the inability for people accurately to judge angles. Pies do not work well for that, so if you need accurately to judge numbers, do not use a pie. Pies work well for “A is about twice as big as B” or “ C is definitely smaller in the second pie”. They are not good for “C is very slightly lower than D” or “B is just under 33%”. Stating it positively:

Use a Pie if the goal is to make broad comparisons, not detailed ones.

Finally, I’d offer a third suggestion, rather than a rule. It’s based on the observation that a bar chart (a natural competitor to a pie chart) is very often improved by ordering — high to low values, for example. Pies can often look radically different when categories are re-ordered, and although it is sometimes suggested that you do this ordering for pies, I think that a pie for categories that can be re-ordered would almost certainly look better in another form. Instead I would suggest the following:

Use a Pie when the categories have a natural order

When Pie Charts Work Well

Stephen Few (Save the pies for Dessert: quotes a study showing that when pies have been shown to be actively superior to bar charts — it is when it makes sense to want to compare sums of categories (e.g. the sum of the first two against the sum of the second two); the reason being that in a pie, you can compare angles for multiple segments easily, whereas in a bar chart that is not easy. 

Survey Data: Bar Chart and Pie Chart

Survey Data: Bar Chart and Pie Chart

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Vega: A New Grammar-Based Specification for Visualizations

I’m a big fan of using languages for visualization rather than canned chart types. I’ve been working with the Grammar of Graphics approach for a number of years within SPSS and now IBM, and my book “Visualizing Time” is composed 95% of Grammar-based visualizations. It’s pretty safe to say it’s my preferred approach.

Protovis (the forerunner of D3, to a great extent) was built on Grammar approach; Bostock and Heer’s 2009 article (on Heer’s site at gives a very good statement of the benefits of the Grammar-based approach as opposed to the “Chart Type” approach:

The main drawback of [the chart type] approach is that it requires a small, closed system. If the desired chart type is not supported, or the desired visual parameter is not exposed in the interface, no recourse is available to the user and either the visualization design must be compromised or another tool adopted. Given the high cost of switching tools, and the iterative nature of visualization design, frequent compromise is likely.

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From the Vaults: How to Speak Visualization

In English, we use many different words to describe the same basic objects. In one survey, researchers Dieth and Orton explored which words were used for the place where a farmer might keep his cow, depending on where the speaker resided in England. The results include words like byreshipponmistallcow-stablecow-housecow-shedneat-house or beast-house. We see the same situation in visualization, where a two-dimensional chart with data displayed as a collection of points, using one variable for the horizontal axis and one for the vertical, is variously called ascatterplot, a scatter diagram, a scatter graph, a 2D dotplot or even a star field.

There have been a number of attempts to form taxonomies, or categorizations, of visualizations. Most software packages for creating graphics, such as Microsoft Excel focus on the type of graphical element used to display the data and then sub-classify from that. This has one immediate problem in that plots with multiple elements are hard to classify (should we classify a chart with a bars and points as a bar chart, with point additions, or instead classify it as a point char, with bars added?). Other authors have started with the dimensionality of the data (one-dimensional, two-dimensional, etc.) and used that as a basic classification criterion, but that has similar problems.

Visualizations are too numerous, too diverse and too exciting to fit well into a taxonomy that divides and subdivides. In contrast to the evolution of animals and plants, which did occur essentially in a tree-like manner, with branches splitting and sub-splitting, information visualization techniques have been invented more by a compositional approach. We take a polar coordinate system, combine it with bars, and achieve a Rose diagram. We put a network in 3D. We addtexture, shape and size mappings to all the above. We split it into panels. This is why a traditional taxonomy of information visualization is doomed to be unsatisfying. It is based on a false analogy with biology and denies the basic process by which visualizations have been created: composition.

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